Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2766)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=11/2, b₁=7/2

http://functions.wolfram.com/07.25.03.2766.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {7/2, 5}, z] == (1/(1527701175 z^2)) (32 E^(z/2) (-3465 + 34650 z + 48073410 z^2 - 104522880 z^3 + 74963280 z^4 - 23183136 z^5 + 3341600 z^6 - 217856 z^7 + 5120 z^8) BesselI[0, z/2]) - (1/(1527701175 z^3)) (64 E^(z/2) (-6930 + 69300 z + 665280 z^2 + 3743355 z^3 - 27943440 z^4 + 28089648 z^5 - 10076480 z^6 + 1565712 z^7 - 106368 z^8 + 2560 z^9) BesselI[1, z/2])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]